Showing papers in "Physical Review C in 1978"
TL;DR: In this article, a coordinate-space method is developed to solve the three-dimensional time-dependent Hartree-Fock equations, which is applied to the study of 16O + 16O collisions at Elab = 105 MeV for incident angular momenta from O to 40h.
Abstract: A coordinate-space method is developed to solve the three-dimensional time-dependent Hartree-Fock equations. It is applied to the study of 16O + 16O collisions at Elab=105 MeV for incident angular momenta from O to 40h. We find fusion for L=13h through 27h and highly inelastic scattering for L≤12h.
NUCLEAR REACTIONS 16O(16O,x) in three-dimensional time-dependent Hartree-Fock approximation. Fusion and strongly damped collisions.
160 citations
TL;DR: In this article, a polyisotopic sodium beam produced by reactions of 20 GeV protons in an uranium target, was illuminated with a tunable cw dye laser and analyzed by a six-pole magnet, ionized, and detected after selection of one isotope by use of a mass spectrometer.
Abstract: A polyisotopic sodium beam produced by reactions of 20 GeV protons in an uranium target, was illuminated with a tunable cw dye laser The atomic beam is analyzed by a six-pole magnet, ionized, and detected after selection of one isotope by use of a mass spectrometer From the optical ${D}_{1}$ resonance lines the hyperfine structure, magnetic moments, and isotope shifts of $^{21\ensuremath{-}31}\mathrm{Na}$ have been determined The nuclear spins of $^{26\ensuremath{-}30}\mathrm{Na}$ have been measured by magnetic resonance The results are discussed in terms of nuclear deformation The analysis of isotope shifts shows the presence of an appreciable volume shift contributionNUCLEAR STRUCTURE $^{26\ensuremath{-}30}\mathrm{Na}$; measured $J$ $^{21\ensuremath{-}31}\mathrm{Na}$; measured isotope shifts; deduced $\ensuremath{\mu}$ Atomic beam laser spectroscopy and magnetic resonance
155 citations
TL;DR: In this paper, a model of the formation of composite nuclei observed in relativistic heavy-ion collisions is developed, which is analogous to that used in accounting for the creation of nuclei under explosive conditions, as encountered in the expansion of an isotropic and homogeneous universe and in imploding-exploding supermassive stars.
Abstract: A description of the formation of composite nuclei observed in relativistic heavy-ion collisions is developed. The description is analogous to that used in accounting for the formation of nuclei under explosive conditions, as encountered in the expansion of an isotropic and homogeneous universe and in imploding-exploding supermassive stars. The model studied is one in which composite nuclei are formed in the space-time evolution of a rapidly expanding system of nucleons. Within the framework of this model, it is shown that reaction rates may initially be fast compared to expansion time scales, that detailed balance can then be met, and a quasi-equilibrium established for a short period of time and limited volume of space in this space-time evolution. An idealized equilibrium model is then proposed which contains a sharp cutoff from equilibrium to free expansion. In such a model the observed properties of the composite particles reflect a ''frozen in'' equilibrium state. A simple discussion is then presented showing that the volume at which the transition occurs is related to the finite size of the correlated structures in the system. A key result in the approach developed is that properties of the composite particle cross sections can be used to obtainmore » information on the size of the emitting region without resorting to a Hambury-Brown--Twiss correlation measurement. Another important result is that cross sections for composite nuclei are characterized by Maxwell-Boltzmann distributions is some rest system and recent data will be discussed from this viewpoint. The thermodynamic properties of the system, such as the equation of state and the energy-temperature relationship are investigated. The effect of continuum correlations from resonances and echoes will also be discussed.« less
140 citations
TL;DR: In this paper, the authors measured total cross sections for protons, dueterons, $\ensuremath{\alpha}$ particles, and $12}\mathrm{C}$ on hydrogen, deuterium, helium, and carbon targets at 1.55 and 2.89 GeV/c nucleon, respectively.
Abstract: We have measured total cross sections for protons, dueterons, $\ensuremath{\alpha}$ particles, and $^{12}\mathrm{C}$ on hydrogen, deuterium, helium, and carbon targets at 1.55 and 2.89 GeV/c nucleon using the "good geometry" transmission method. In addition, we measured the inelastic cross sections and elastic slope parameters for reactions initiated by deuterons, $\ensuremath{\alpha}$ particles, and $^{12}\mathrm{C}$. Our results are in good agreement with Glauber theory predictions, but the factorization relation ${\ensuremath{\sigma}}_{T}(\mathrm{AA})=\frac{{[{\ensuremath{\sigma}}_{T}(\mathrm{AB})]}^{2}}{{\ensuremath{\sigma}}_{T}(\mathrm{BB})}$ is not a good guide. We find ${\ensuremath{\sigma}}_{T}\ensuremath{\simeq}144{({{A}_{T}}^{\frac{1}{3}}\ensuremath{-}{{A}_{p}}^{\frac{1}{3}}\ensuremath{-}1.48)}^{2}$ mb and ${\ensuremath{\sigma}}_{\mathrm{IN}}\ensuremath{\simeq}78{({{A}_{T}}^{\frac{1}{3}}+{{A}_{p}}^{\frac{1}{3}}\ensuremath{-}1.25)}^{2}$ mb, where ${A}_{T}({A}_{p})$ is the atomic mass number of the target (projectile).NUCLEAR REACTIONS $^{12}\mathrm{C}(^{12}\mathrm{C}, X)$, ($\ensuremath{\alpha}, X$), ($d, X$), ($p, X$), $E=0.87 \mathrm{and} 2.10$ GeV/nucleon; measured total cross section, total inelastic cross section, and slope parameter of elastic scattering.
116 citations
TL;DR: In this article, a mean-field approximation of 236U is calculated in the time-dependent mean field approximation assuming axial and reflection symmetry and omitting the spin-orbit interaction.
Abstract: Induced fission of 236U is calculated in the time-dependent mean-field approximation assuming axial and reflection symmetry and omitting the spin-orbit interaction. Constrained static solutions are used to generate the appropriate initial condition and are compared in detail with results of macroscopic-microscopic calculations. Although dynamic mean-field results are strongly dependent upon an effective pairing gap, predicted observables are consistent with experiment for plausible values of the gap. Detailed comparisons with macroscopic models indicate that both a modified one-body dissipation and two-body viscosity yield observables similar to those of the mean-field theory, even though these physical dissipation mechanisms are fundamentally different.
92 citations
TL;DR: In this paper, a comparative study of the fragmentation of nuclei in nuclear emulsion has been made by using nuclear detectors, and the mean free paths (cm) for these nuclei are 21.7, 13.5, and 13.8, respectively.
Abstract: A comparative study of the fragmentation of $^{4}\mathrm{He}$, $^{12}\mathrm{C}$, $^{14}\mathrm{N}$, and $^{16}\mathrm{O}$ nuclei, $E=2.1$ GeV/nucleon, has been made by using nuclear emulsion detectors. The interaction mean-free paths (cm) for these nuclei in emulsion are 21.8 \ifmmode\pm\else\textpm\fi{} 0.7, 13.8 \ifmmode\pm\else\textpm\fi{} 0.5, 13.1 \ifmmode\pm\else\textpm\fi{} 0.5, and 13.0 \ifmmode\pm\else\textpm\fi{} 0.5, respectively. These data are discussed in terms of optical models and geometrical theories. Fragmentation reactions initiated by $^{12}\mathrm{C}$, $^{14}\mathrm{N}$, and $^{16}\mathrm{O}$ projectiles that exhibit no target excitation, i.e., that possess no low energy particle emission. are selected for special study of projectile fragmentation. The projected angular distributions of $Z=1 \mathrm{and} 2$ secondaries from these interactions are reported, as are the prong-number and charge-multiplicity distributions. The angular distributions are independent of the projectile and exhibit features of limiting fragmentation.NUCLEAR REACTIONS Emulsion exp., $^{4}\mathrm{He}$, $^{12}\mathrm{C}$, $^{14}\mathrm{N}$, and $^{16}\mathrm{O}$ at 2.1 GeV/A; measured mean-free-path lengths; projectile fragmentation reactions; angular, number, and charge multiplicity distributions. Optical and geometrical models; limiting fragmentation.
88 citations
TL;DR: Fission product yields for 44 masses were determined for the fission of $^{238}\mathrm{U}$ with essentially monoenergetic neutrons of 1.5, 2.0, 3.9, 5.9 and 7.7 MeV as discussed by the authors.
Abstract: Fission product yields for 44 masses were determined for the fission of $^{238}\mathrm{U}$ with essentially monoenergetic neutrons of 1.5, 2.0, 3.9, 5.5, 6.9, and 7.7 MeV. Fission product activities were measured by Ge(Li) $\ensuremath{\gamma}$-ray spectrometry of irradiated $^{238}\mathrm{U}$ foils and by chemical separation of the fission product elements followed by $\ensuremath{\beta}$ counting and/or $\ensuremath{\gamma}$-ray spectrometry. The mass-yield data for $^{238}\mathrm{U}(n,f)$ show clearly the sensitive exponential increase of fission yields in the near-symmetric mass region (valley) with increasing incident neutron energy ${E}_{n}$ (peak-to-valley ratio decreasing from \ensuremath{\sim}600 to \ensuremath{\sim}40) over the range ${E}_{n}=1.5 \mathrm{to} 7.7$ MeV with little change in yields in other regions of the mass distribution. The valley yields plotted semilogarithmically as a function of ${E}_{n}$ reveal an abrupt change in slope at the onset of second-chance fission just above the neutron binding energy (at \ensuremath{\sim}6 MeV) where the excitation energy is lowered by competition with neutron evaporation prior to fission. Systematics are developed to permit synthesis of the mass distribution for any neutron energy in the range of 1.5 to 18 MeV.[NUCLEAR REACTIONS, FISSION $^{238}\mathrm{U}(n,f) {E}_{n}=1.5,2.0,3.9,5.5,6.9,\mathrm{and} 7.7$ MeV; measured mass yields.]
84 citations
TL;DR: In this article, a semi-empirical nuclear level density formula is proposed, which takes into account the influence of nuclear shell structure on level densities and the excitation energy dependence of shell effects.
Abstract: A new semiempirical nuclear level density formula is proposed, which takes into account the influence of nuclear shell structure on level densities and the excitation energy dependence of shell effects. The ground state shell and pairing energies enter directly into this formula, which involves three mass-independent parameters characterizing the average single-particle level density near the Fermi level and the wavelength of shell oscillations. The present formulation is shown not only to give a good fit to the experimental data on neutron resonance spacings of spherical nuclei, but also to provide a reliable extrapolation to higher excitation energies. The present analysis has also brought out the need to include the dependence of level density parameter a on the surface to volume ratio of nuclei. The analysis of the data for deformed nuclei with the present formulation does not indicate an enhancement of the level densities of the magnitude suggestive of a rotation degree of freedom completely decoupled from intrinsic degrees at the excitation energy equal to neutron binding energies.
84 citations
TL;DR: In this article, the authors present an approach to the treatment of Coulomb effects in atomic and nuclear reactions of the three-body type in which two of the particles are charged.
Abstract: We present the details of a novel approach to the treatment of Coulomb effects in atomic and nuclear reactions of the three-body type in which two of the particles are charged. Based on three-body integral equations the formalism allows the practical calculation of elastic, inelastic, rearrangement, and breakup processes with full inclusion of the Coulomb repulsion or attraction in a mathematically correct way. No restrictions need to be made concerning the form of the short-range interactions between the three pairs. A particular virtue of our method lies in the fact that it corroborates, and gives precise meaning to, the intuitively anticipated conception of how to describe such reactions.
84 citations
TL;DR: In this article, the 2.1- and 4.9-GeV proton irradiation of C, Al, Ag, and U targets were measured at several angles to the beam for products ranging from He up to Ar for the heavier targets.
Abstract: Fragment energy spectra from the 2.1- and 4.9-GeV proton irradiation of C, Al, Ag, and U targets were measured at several angles to the beam for products ranging from He up to Ar for the heavier targets. The fragments were detected in a telescope consisting of a gas $\ensuremath{\Delta}E$ counter and a silicon $E$ counter. The carbon target measurements are compared with previous data from projectile fragmentation studies. A Maxwellian type functional form which fits the energy spectra from all the targets is presented. The spectra were integrated to obtain values of the cross section as a function of atomic number.
83 citations
TL;DR: In this article, the relativistic Hartree and Hartree-Fock equations are applied to nuclei with different one-boson exchange potentials as well as the effective interaction of Walecka, introduced in his theory of highly condensed matter.
Abstract: A relativistic nuclear Hamiltonian is constructed, from which the relativistic Hartree and Hartree-Fock equations are derived. Then the Hartree equations are applied to $^{16}\mathrm{O}$ and $^{40}\mathrm{Ca}$ nuclei taking as input different relativistic one-boson-exchange potentials as well as the effective interaction of Walecka, introduced in his theory of highly condensed matter. Single-particle energies turn out to be of the correct magnitude. In particular, it is possible to explain the magnitude of the spin-orbit splitting without any free parameter.NUCLEAR STRUCTURE $^{16}\mathrm{O}$, $^{40}\mathrm{Ca}$; calculated single-particle binding energies. Relativistic Hartree-Fock method.
TL;DR: In this paper, a model is presented which is capable of calculating simultaneously the spectra of pions, nucleons, and light nuclei from the collision of relativistic heavy ions based on the nuclear thermodynamics of Mekjian and Kapusta.
Abstract: A model is presented which is capable of calculating simultaneously the spectra of pions, nucleons, and light nuclei from the collision of relativistic heavy ions It is based on the nuclear thermodynamics of Mekjian and Kapusta Maximum use is made of the conservation laws for baryon number, charge, energy, momentum, and angular momentum Single particle inclusive cross sections were calculated and compared with experiment for a wide range of beam energies and observed fragments Except for some conflicting normalizations and high-energy pions good agreement is found The density at which hadrons effectively cease to interact, which is the only parameter in the model, is determined to be 012 hadrons/${\mathrm{fm}}^{3}$NUCLEAR REACTIONS Relativistic heavy ions; firestreaks, hadronic thermal equilibrium; calculated differential cross sections of ${\ensuremath{\pi}}^{\ifmmode\pm\else\textpm\fi{}}$, $p$, $d$, $t$, $^{3}\mathrm{He}$, $^{4}\mathrm{He}$; comparisons with experiment
TL;DR: In this article, an extensive optical model analysis of these elastic scattering cross sections and other available data, using squared Woods-Saxon form factors, results in potentials with fixed geometry for both real and imaginary parts and depths with smooth energy behavior over a broad incident energy range.
Abstract: Angular distributions for alpha -particle elastic scattering by /sup 40,44/Ca and excitation of the 3.73 MeV 3/sup -/ collective state of /sup 40/Ca were measured for incident energies ranging from 40 to 62 MeV. An extensive optical model analysis of these elastic scattering cross sections and other available data, using squared Woods-Saxon form factors, results in potentials with fixed geometry for both real and imaginary parts and depths with smooth energy behavior over a broad incident energy range. These results are discussed in the frame of the semi-classical approximation developed by Brink and Takigawa (1977). The sensitiveness of the calculated elastic scattering cross sections to the real part of the potentials as a function of the projectile-target distance has been investigated by means of a notch test. Distorted-wave Born-approximation calculations for the excitation of the 3.73 MeV 3/sup -/ state of /sup 40/Ca are presented.
TL;DR: In this paper, an analytic function of energy is fitted to the available $S, $P, and $D$ wave $\ensuremath{pi}N$ phase shifts of various goups below 400 MeV.
Abstract: An analytic function of energy is fitted to the available $S$, $P$, and $D$ wave $\ensuremath{\pi}N$ phase shifts of various goups below 400 MeV. This global average, which reproduces well most of the experiment cross sections, is anticipated to be useful in pion-nucleus and pion-nucleon interaction calculations.
TL;DR: The mass excesses of /sup 16/Ne, /sup 15/F, and /sup 12/O were determined to be 23.92 +- 0.08, 16.67 + 0.18, and 32.12 MeV, respectively as discussed by the authors.
Abstract: The (/sup 4/He,/sup 8/He) and (/sup 3/He,/sup 8/Li) reactions have been employed at detection angles near 8/sup 0/ on gas targets of /sup 20/Ne and /sup 16/O to produce and measure the masses of the nuclei /sup 16/Ne, /sup 15/F, and /sup 12/O. The (/sup 4/He, /sup 8/He) reactions were performed at an incident energy of 117 MeV, and the (/sup 3/He, /sup 8/Li) reaction was done at 88 and 75 MeV. The mass excesses of /sup 16/Ne, /sup 15/F, and /sup 12/O were determined to be 23.92 +- 0.08, 16.67 +- 0.18, and 32.10 +- 0.12 MeV, respectively. Estimated ground state decay widths were GAMMA/sub c.m./ = 0.2 +- 0.1, 0.8 +- 0.3, and 0.40 +- 0.25 MeV, for /sup 16/Ne, /sup 15/F, and /sup 12/O, respectively. A d coefficient of 8 +- 5 keV is indicated for the isobaric multiplet mass equation description of the mass-16 multiplet. Consideration of the possible decay mechanisms of /sup 16/Ne and /sup 12/O indicates that both nuclei probably have an appreciable diproton decay width.
TL;DR: In this paper, a two-fluid dynamical model is introduced to take into account the expected partial transparency of nuclei during collisions at high energy, in which coupled relativistic equations of motion are solved for separate target and projectile nuclear fluids.
Abstract: To take into account the expected partial transparency of nuclei during collisions at high energy, we introduce a two-fluid dynamical model, in which coupled relativistic equations of motion are solved for separate target and projectile nuclear fluids. At low relative velocities the target and projectile fluids merge, in which case the conventional one-fluid dynamical model is recovered. For given nuclear equation of state and initial conditions, the equations of motion are solved as functions of time for the nucleon number density, momentum density, energy density, pressure, and velocity for each fluid. In spatial dimensions by means of a relativistic generalization of a standard particle-in-cell finite-difference computing method for multiphase fluid-dynamics problems. For each of several impact parameters, the velocity distribution at some large time is converted to an energy and angular distribution for the expanding matter. Integration of these results over impact parameter then gives d/sup 2/sigma/dEd..cap omega... For /sup 20/Ne + /sup 238/U at laboratory bombarding energies per nucleon of 250 MeV, 400 MeV, and 2.1 GeV, as well as for /sup 4/He + /sup 238/U at a laboratory bombarding energy per nucleon of 400 MeV, we compare calculated and experimental energy spectra for outgoing charged particles at severalmore » angles. The calculations reproduce correctly the experimental slopes at each angle, as well as the overall decrease in the experimental cross section when going from forward to backward angles. However, for /sup 20/Ne + /sup 238/U at laboratory bombarding energies per nucleon of 250 and 400 MeV, the calculated values at 30/sup 0/ are only one-third the experimental values. Also, for /sup 4/He + /sup 238/U at a laboratory bombarding energy per nucleon of 400 MeV, the calculated values at all angles are substantially smaller than the experimental values. We deduce results for /sup 238/U + /sup 238/U at laboratory bombarding energies per nucleon of 250 MeV and 2.1 GeV.« less
TL;DR: In this article, the angular and momentum distributions of fragments emitted from central collisions between emulsion nuclei (AgBr) and heavy-ion projectiles /sup 4/He, /sup 1/6O, and /sup4/0Ar at beam rigidity 5.72 GV were analyzed in terms of a modified Maxwell-Boltzmann distribution.
Abstract: We have performed an experimental study of the angular and momentum distributions of fragments emitted from central collisions between emulsion nuclei (AgBr) and heavy-ion projectiles /sup 4/He, /sup 1/6O, and /sup 4/0Ar at beam rigidity 5.72 GV. Central collisions are here defined as interactions that exhibit an absence of projectile fragmentation, i.e., no beam-velocity fragments are produced within 5/sup 0/ of the incident beam direction. Production angles have been measured for all fragments having a restricted gain density g > or = 2g/sub min/, corresponding to protons of E < or = 250 MeV. Both range and angle measurements have been made for fragment ranges < or = 4 mm, corresponding to protons of E < or = 31 MeV. The data are analyzed in terms of a modified Maxwell-Boltzmann distribution from which we obtain estimates of the longitudinal velocity ..beta../sub parallel/ and the characteristic spectral volocity ..beta../sub 0/ of the particle-emitting systems. We find that no unique Maxwellian distribution can account for the observed fragment distributions. The angular distributions do not display statistically significant structure attributable to collective phenomena.
TL;DR: In this paper, a hierarchy of approximations to the many-body Schroedinger equation is presented which reduces to the time-dependent mean-field approximation in lowest order and provides systematic corrections in subsequent orders.
Abstract: A general hierarchy of approximations to the many-body Schroedinger equation is presented which reduces to the time-dependent mean-field approximation in lowest order and provides systematic corrections in subsequent orders. The theory is applied to two interacting systems described by the Lipkin model Hamiltonian. Comparison of the results of the lowest two orders of approximation with the exact solution demonstrates the practicality of the method and its potential for generalizing nuclear dynamics beyond the mean field theory.
TL;DR: In this paper, a simple extension of the Glauber high energy approximation is used to study the effects of nuclear correlations on the optical phase shift function of nucleon-nucleon total cross-sections.
Abstract: Collisions between nuclei are studied by means of a simple extension of the Glauber high energy approximation. An expression for the optical phase shift function, exact within the framework of the Glauber approximation, is expanded in an infinite series and includes the effects of nuclear correlations. The first term corresponds to the standard optical limit result of the Glauber theory, and the higher order corrections arise from the processes in which one or more nucleons of either nucleus can undergo multiple collisions. The center-of-mass correlation is treated consistently so that our results do not exhibit the large-q divergence which characterizes the usual optical limit. It is shown that with realistic constraints on nucleon-nucleon total cross sections, the optical phase shift function does not approach the usual optical limit result when the mass numbers of the colliding nuclei become very large. With a proper treatment of center-of-mass correlations, the optical phase shift series converges rapidly for light nuclei and allows one to perform realistic calculations. The effects of higher order corrections on total and inelastic cross sections and on elastic scattering intensities are examined. The effects of the Coulomb field are included in an average phase approximation and results are comparedmore » with measurements.« less
TL;DR: In this paper, three-dimensional time-dependent Hartree-fock calculations for the fusion excitation functions are presented, and the low-energy fusion cross sections obtained for this system demonstrate the sensitivity of time dependent HartreeFock calculations to the effective interaction used.
Abstract: Three-dimensional time-dependent Hartree-Fock calculations for the $^{16}\mathrm{O}$ + $^{16}\mathrm{O}$ and $^{40}\mathrm{Ca}$ + $^{40}\mathrm{Ca}$ fusion excitation functions are presented. Results for the former system are in good agreement with experiment for ${E}_{\mathrm{lab}}\ensuremath{\le}120$ MeV and indicate a dynamical lower angular momentum limit to fusion for ${E}_{\mathrm{lab}}\ensuremath{\ge}54$ MeV. Results for $^{40}\mathrm{Ca}$ + $^{40}\mathrm{Ca}$ are compared with previous two-dimensional calculations. The low-energy fusion cross sections obtained for this system demonstrate the sensitivity of time-dependent Hartree-Fock calculations to the effective interaction used.
TL;DR: In this article, a momentum space method for hadronic atoms is developed to incorporate relativistic, nonlocal, complex hadron-nucleus interactions, and the logarithmic singularity due to the Coulomb interaction is treated by Lande's subtraction technique.
Abstract: A momentum space method for hadronic atoms is developed to incorporate relativistic, nonlocal, complex hadron-nucleus interactions. The logarithmic singularity due to the Coulomb interaction has been treated by Lande's subtraction technique. Vacuum polarization, and both nuclear and pion finite-size effects have been included in this momentum space method. Precision eigenvalues and eigenfunctions for the Schr\"odinger, relativistic Schr\"odinger, Klein-Gordon (of various types), and Dirac equations have been calculated using a rapid and convenient inverse iteration method. Reliability of this novel approach is confirmed by comparing with parallel coordinate space methods. Several illustrative applications are made to simple pionic, and kaonic cases to demonstrate possible applications. For example, it is found that: (1) to extract the pion size from pionic atom data, energy shifts must be measured to an accuracy of better than 50 eV; (2) to determine the form of Klein-Gordon equations appropriate for kaonic atoms, one needs a precision of better than 20 eV; (3) the finite-range of the $\ensuremath{\pi}\ensuremath{-}N$ interaction plays a non-negligible role and, therefore, should be carefully included in the pion-nucleus interaction. More extensive applications of these methods are suggested.NUCLEAR STRUCTURE Hadronic atoms, momentum space formulation, and its applications.
TL;DR: In this article, the first order spin-dependent microscopic proton-nucleus optical potential of Kerman, McManus, and Thaler was used to analyze 800 MeV polarized proton elastic differential cross section and analyzing power data for target nuclei.
Abstract: The first order, spin-dependent microscopic proton-nucleus optical potential of Kerman, McManus, and Thaler is used to analyze 800 MeV polarized proton elastic differential cross section and analyzing power data for target nuclei $^{58}\mathrm{Ni}$, $^{90}\mathrm{Zr}$, $^{116,124}\mathrm{Sn}$, and $^{208}\mathrm{Pb}$. Approximately model-independent target neutron density distributions are constructed in order to investigate the uncertainty in the deduced neutron densities resulting from the statistical error and the finite range of momentum transfer in the experimental angular distributions. Numerous other experimental and theoretical sources of error and uncertainty are considered to obtain a realistic estimate of the total error in the deduced neutron densities and their root-mean-square radii. The typical error in the root-mean-square radii is found to be \ifmmode\pm\else\textpm\fi{}0.07 fm. Impressive qualitative agreement is found between the deduced neutron matter densities and the corresponding densities predicted by Hartree-Fock calculations.NUCLEAR REACTIONS Proton-nucleus scattering, $E=0.8$ GeV; targets $^{58}\mathrm{Ni}$, $^{90}\mathrm{Zr}$, $^{116,124}\mathrm{Sn}$, $^{208}\mathrm{Pb}$; analyzing power; spin-dependent Kerman, McManus, and Thaler optical potential; model-independent densities; error analysis; neutron radii.
TL;DR: In this paper, the mass and charge distributions for the heavy target residues from relativistic heavy ion reactions are carried out for the reaction of $12, C, U, Pb, Ag, and Cu and compared with experimental data.
Abstract: Calculations of the mass and charge distributions for the heavy target residues from relativistic heavy ion reactions are carried out for the reaction of $^{12}\mathrm{C}$ with $^{238}\mathrm{U}$, $^{208}\mathrm{Pb}$, $^{197}\mathrm{Au}$, Ag, and Cu and compared with experimental data. The primary product distributions are calculated using the abrasion-ablation model. Nuclear charge distributions are calculated using either a stochastic model or a model based upon the zero-point oscillations of the giant dipole resonance. Standard statistical deexcitation calculations are used to calculate secondary product distributions. The results show that some of the principal features of the residue mass and charge distributions can be accounted for with the simple assumptions of the abrasion-ablation model and the assumption that product charge distributions are due to the sudden nature of the interaction and the zero-point oscillations of the giant dipole resonance.
TL;DR: In this paper, the authors measured the 0.ifmmode,circ\circ\else\textdegree\fi{} neutron spectra resulting from 800 MeV proton bombardment of targets of Al, Ti, Cu, W, Pb and U have been measured for momenta above 500 MeV/c.
Abstract: The 0\ifmmode^\circ\else\textdegree\fi{} neutron spectra resulting from 800 MeV proton bombardment of targets of Al, Ti, Cu, W, Pb, and U have been measured for neutron momenta above 500 MeV/c. Integrated cross sections for the quasielastic charge exchange peaks and the broad pion associated peaks at lower momenta show a remarkably smooth dependence on atomic mass of the target, varying as ${A}^{\frac{2}{3}}$ and ${A}^{\frac{1}{2}}$, respectively.
TL;DR: In this paper, the importance of the ($n,{n}^{\ensuremath{'}}p$) reaction as a source of protons is examined by comparing these results with those recently obtained for $^{46}\mathrm{Ti}$.
Abstract: Cross sections for the ($n,xp$), ($n,d$), and ($n,x\ensuremath{\alpha}$) reactions for 15-MeV neutrons on $^{51}\mathrm{V}$ and $^{93}\mathrm{Nb}$ have been measured with a magnetic quadrupole spectrometer. The importance of the ($n,{n}^{\ensuremath{'}}p$) reaction as a source of protons is examined by comparing these results with those recently obtained for $^{46}\mathrm{Ti}$. Good fits to the ($n,xp$) and ($n,x\ensuremath{\alpha}$) energy spectra require contributions from both equilibrium and nonequilibrium reactions, while only the latter appear in the ($n,d$) spectra. Calculated values for the ($n,{n}^{\ensuremath{'}}p$) and ($n,{n}^{\ensuremath{'}}\ensuremath{\alpha}$) cross sections agree well with the experimental values. The cross sections are $^{51}\mathrm{V}(n,xp)$ 91 \ifmmode\pm\else\textpm\fi{} 14 mb, $^{51}\mathrm{V}(n,xd)$ 7 \ifmmode\pm\else\textpm\fi{} 3 mb, $^{51}\mathrm{V}(n,x\ensuremath{\alpha})$ 17 \ifmmode\pm\else\textpm\fi{} 3 mb, $^{93}\mathrm{Nb}(n,xp)$ 51 \ifmmode\pm\else\textpm\fi{} 8 mb, $^{93}\mathrm{Nb}(n,xd)$ 8 \ifmmode\pm\else\textpm\fi{} 3 mb, and $^{93}\mathrm{Nb}(n,x\ensuremath{\alpha})$ 14 \ifmmode\pm\else\textpm\fi{} 3 mb.
TL;DR: In this article, the distribution of isoscalar octupole strength in 18 nuclei from $40} to $208} was studied and a prominent broad peak was observed in this excitation energy range.
Abstract: Beams of 96 and 115 MeV $\ensuremath{\alpha}$ particles have been used to study the distribution of isoscalar octupole strength in 18 nuclei from $^{40}\mathrm{Ca}$ to $^{208}\mathrm{Pb}$. A prominent broad peak ($\ensuremath{\Gamma}\ensuremath{\sim}2.5$ MeV) is observed at ${E}_{x}\ensuremath{\sim}\frac{30}{{A}^{\frac{1}{3}}}$ MeV in nuclei from $^{66}\mathrm{Zn}$ to $^{197}\mathrm{Au}$. No broad peak is observed in this excitation energy range in $^{208}\mathrm{Pb}$ or $^{40}\mathrm{Ca}$ and lighter nuclei. The oscillatory angular distributions of the ($\ensuremath{\alpha}, {\ensuremath{\alpha}}^{\ensuremath{'}}$) reaction exciting this peak are in excellent agreement with $l=3$ distorted-wave Born approximation calculations. Studies of the angular range from ${\ensuremath{\sigma}}_{\mathrm{lab}}=3.5\ifmmode^\circ\else\textdegree\fi{} \mathrm{to} 6\ifmmode^\circ\else\textdegree\fi{}$ in $^{116}\mathrm{Sn}$ indicate very little contribution from $l=1$ strength. Energy- weighted sum rule fractions for this low-energy octupole resonance are generally in the range from 15% to 20%; this corresponds to \textonehalf{} to $\frac{2}{3}$ of the expected $1\ensuremath{\hbar}\ensuremath{\omega}$ octupole strength. The overall distribution of octupole strength in spherical nuclei, including the absence of the low-energy octupole resonance in $^{40}\mathrm{Ca}$ and $^{208}\mathrm{Pb}$, is in very good agreement with random-phase approximation calculations. The low-energy octupole resonance undergoes a pronounced change in structure in soft-vibrational and deformed nuclei. Theoretical calculations for the low-energy octupole resonance in $^{154}\mathrm{Sm}$ account qualitatively for the data.
TL;DR: In this paper, a study of the (t,p) reactions on /sup 4/He, /sup 6/Li, etc., was carried out using 23 MeV tritons and an Elbek-type spectrograph using photographic emulsions as detectors.
Abstract: A study of the (t,p) reactions on /sup 4/He, /sup 6/Li, /sup 7/Li, /sup 9/Be, /sup 1/0B, /sup 1/1B, and /sup 1/2C has been carried out using 23 MeV tritons and an Elbek-type spectrograph using photographic emulsions as detectors. A total of 71 states of /sup 6/He, /sup 8/Li, /sup 9/Li, /sup 1/1Be, /sup 1/2B, /sup 1/3B, and /sup 1/4C have been studied. Some of the states had not been previously reported. In other cases new values of excitation energies and widths are proposed. Attempts have been made to fit the 62 angular distributions we obtained with the distorted-wave Born approximation: no systematic analysis was possible except in the case of L = 0 distributions.
TL;DR: In this paper, a detailed optical model analysis of /sup 16/O on /sup 208/Pb elastic data from 80 to 216.6 MeV has been made.
Abstract: Elastic scattering for /sup 16/O on /sup 208/Pb and the single-nucleon transfer reactions /sup 208/Pb(/sup 16/O,/sup 15/N) /sup 209/Bi and /sup 208/Pb(/sup 16/O,/sup 17/O) /sup 207/Pb have been measured at bombarding energies of 104, 138.5, and 216.6 MeV. A detailed optical model analysis of /sup 16/O on /sup 208/Pb elastic data from 80 to 216.6 MeV has been made. The Woods-Saxon potential parameters must be energy dependent to accurately reproduce the elastic data. Finite-range distorted-wave Born-approximation calculations employing both energy- independent and energy-dependent optical potentials are compared with the transfer data. With the exception of small shifts in angle, the distorted-wave Born approximation correctly predicts the shape of the angular distributions and the evolution of the relative single-particle strengths as functions of the bombarding energy. However, the distorted-wave Born approximation fails (by a factor of 2 to 3) to predict the observed energy dependence of the absolute single-particle transfer strength. It is demonstrated that this failure is not likely to be corrected by changes in the bound-state or optical-model potentials, if Woods-Saxon forms that fit the elastic data are used.
TL;DR: In this article, total fusion cross sections sigma/sub F/ have been measured for /sup 16/O + /sup 14/O at bombarding energies 27-66 MeV using the E -..delta..E or the time-of-flight techniques.
Abstract: Total fusion cross sections sigma/sub F/ have been measured for /sup 16/O + /sup 16/O at bombarding energies 27--66 MeV using the E - ..delta..E or the time-of-flight techniques. The fusion excitation function shows oscillatorion in agreement with the resonances produced in the total reaction cross section by a surface-transparent potential. The results are compared to those obtained via the ..gamma..-ray technique and the importance of direct decay to ground states is discussed. Mass and total angular distributions are well reproduced by statistical model calculations which take angular momentum into account explicitly. Barrier and critical parameters are extracted from the average energy behavior of sigma/sub F/. No evidence for shell effects as predicted by Glas and Mosel is found on the measured fusion cross sections.